We will have Sunday afternoon to do something, anything not too far from St Neots worthy, otherwise we may just go to Cambridge...?
Not a country house, but an interesting and important house.
78 Derngate, Northampton
Not been to either despite growing up in Northants.
We had a great time here over Easter - lovely grounds, kids enjoyed the treasure hunt.
http://www.english-heritage.org.uk/visit/places/wrest-park/
For gardens, as well as those above, Anglesey Abbey on the other side of Cambridge is nice. Wimpole is more of a house and farm park, pretty to walk around but not cheap. I guess Burghley House (Stamford) is a bit far for you, but very impressive.
There is plenty of interesting war-time and airforce stuff, like Duxford, Shuttleworth Collection (Biggleswade) and Bletchley Park.
If you just want a walk in the country, you can visit Fen Drayton Lakes or Ouse Washes (Needingworth) for free and then stop for a pint at the Floods Tavern in St Ives (free parking on Sundays at the Waitrose).
Cambridge will be busy and a lot of the museums are closed on Sundays (and Mondays) but it's nice to walk around if you've never been before.
Cambridge botanical gardens is lovely. great cafe too.
Shuttleworth has the air museum etc plus lovely gardens too.See here....